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Complementarily Transforming Jitterbugs

Last revision: October 20, 2011

This is a Java-based interactive viewer to allow you to further investigate the jitterbug transformation. Look at the original Jitterbug viewer if you haven't already.

The two extreme phases of the jitterbug (the octahedron and the vector equilibrium) complement each other to form an all-space-filling matrix which can also undergo jitterbug transformations. Here two complementarily transforming jitterbugs are joined to help you envision this process.

In this coupled configuration, each jitterbug has only half the range of motion as it does when uncoupled. Rather than move from an octahedron through a vector equilibrium to another octahedron, as they are free to do when uncoupled, they move from an octahedron to a vector equilibrium and then back to the same octahedron. When one is in its octahedron phase, the other is in its vector equilibrium phase.


Things start out in "Animate" mode which means the jitterbugs are continuously moving through their various stages. Selecting the "Step" option (or clicking the "Step" button) stops the movement, or, if it is already stopped, moves the jitterbugs slightly toward their next stage.

In the "Step" mode, extra lines appear at certain stages:

Any of these distinctive stages can also be selected directly from the list of options.

Selecting the "Animate" option (or clicking the "Animate" button) starts up the continuous movement again. Choosing this option several times in a row will speed up the animation. In the animation mode, the extra lines never appear.

The jitterbugs can be rotated at any time (animated or not) by pressing down the left mouse button while the mouse is in the viewing area and moving the mouse in the desired direction of rotation.

The Jitterbugs

Additional Notes

I like to maneuver the jitterbugs into an interesting orientation while it is stopped and then animate it or select different stages to see how the jitterbug appears at different stages while in that orientation.

Making the jitterbugs' hinges fixed is a rather artificial assumption, but one it seems difficult to escape with many physical models. With a graphical model, it is fairly easy to obtain interesting, and probably more relevant, behaviors by dynamically altering where the jitterbugs are hinged. When this is done, the triangles of both a single jitterbug and the coupled jitterbugs can go through a full 360° cycle of motion. Adrian Rossiter has done some interesting animations with this assumption.

The relevant source code files are, and contains a main() routine for a stand-alone Java application program which duplicates the behavior of the applet, but is resizable as well.

The applet is currently internationalized for de, en, es, fr and nl localities. Your suggestions on translations for these localities or other languages are appreciated. Look over the English template for the phrases I am translating. Thanks to Val Gůmez JŠuregui for help on the Spanish and his boss for help on the German. Thanks to Jan Marcus for the Dutch translations he supplied.

Contact Information

Your comments and questions are welcome. Send them to:

Bob Burkhardt
Tensegrity Solutions
Box 426164
Cambridge, MA 02142-0021


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